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Solve the given problem using the given method

Solve the given problem using the given method

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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Solve the given problem using the given method

7. Use the method of Lagrange multipliers to find a relative minimum of f(x, y, z) = x² + 4y? + 16z² subject to the constraint cyz = 1. 1. Create the auxiliary function F of four variables x, y, z, and A for which F(x, y, z, a) = f(x, y, z) + Ag(x, y, z) 2. Establish the system of equations obtained by setting the four first partial derivatives of F equal to zero. F.(x, y, z. A) = 0 F,(x. y, z, A) = 0 |F(x, y, z, A) = 0 |F.(x, y, z, A) = 0
Transcribed Image Text:7. Use the method of Lagrange multipliers to find a relative minimum of f(x, y, z) = x² + 4y? + 16z² subject to the constraint cyz = 1. 1. Create the auxiliary function F of four variables x, y, z, and A for which F(x, y, z, a) = f(x, y, z) + Ag(x, y, z) 2. Establish the system of equations obtained by setting the four first partial derivatives of F equal to zero. F.(x, y, z. A) = 0 F,(x. y, z, A) = 0 |F(x, y, z, A) = 0 |F.(x, y, z, A) = 0
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